It should work if configured correctly. Just another thing to check - that your proxy pass rules are accessible within the SSL connection. It is possible to configure the SSL version of a website to be different from the non-SSL version. Make sure that your proxy pass configuration is sitting in both.

In most cases, if the worker has a configuration problem, Apache will answer with a 500
error (Server error). If you get a 404, this is rather because the request does not get passed to the Tomcat server (or the URL is invalid from Tomcat point of view). Check
that the JkMount is present and correct in your Apache configuration (for the 443 port).

To debug problems with mod_jk, turn on the debug logs in mod_jk and look at Apache logs.
Add these lines in mod_jk configuration (jk.conf in general):

JkLogFile /var/log/apache2/mod_jk.log

JkLogLevel debug

You should see some logs at startup and some interesting details for each request.

Look at this article. It explains exactly how to do mod_jk with https. It is accomplished via a secure virtual host which then communicates to Tomcat on the same standard AJP channel you use with non secure connection.